Unbiased Estimation of the Gradient of the log-likelihood for Partially Observed Diffusions

In this work we present a new coupled simulation method for the unb iased estimation of the gradient of the log-likelihood for a class of partially observed diffusion processes. This is of interest in stochastic gradient algorithms, which typically require such unbiasedness. Intrinsically, given only access to standard time-discretizations of diffusion processes (such as Euler), we present a methodology which provides unbiased estimates of gradient of the log-likelihood which has no time-discretization error. This method also provides estimates with finite variance and expected cost. Some preliminary simulation results are also given. This is a joint work with Jeremy Heng (ESSEC Singapore) and Jeremie Houssineau (Warwick).